Volume of Composite Shapes 1

Years

Year 8

Surface Area and Volume

Volume of Composite Shapes

Volume of Composite Shapes 1

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Question 1 of 5

1. Question
Find the volume of the figure
- $\text(Volume )=$ (25200) $\text(cm)^3$
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Volume of a Rectangular Prism

$\text(Volume )=\text(length) times \text(width) times$ $\text(depth)$

Labelling the given lengths

$\text(Smaller Rectangle)$

$\text(length)=30$

$\text(width)=20$

$\text(depth)=12$

$\text(Larger Rectangle)$

$\text(length)=60$

$\text(width)=25$ $(55-$ $30$ $)$

$\text(depth)=12$

First, find the area of the smaller rectangle

$\text(Area)$ $=$ $\text(length)$ $times$ $\text(width)$

$=$ $30$ $times$ $20$ $=$ $600 \text(cm)^2$

Next, find the area of the larger rectangle

$\text(Area)$ $=$ $\text(length)$ $times$ $\text(width)$

$=$ $60$ $times$ $25$ $=$ $1500 \text(cm)^2$

Next, add the area of the smaller rectangle and the area of the larger rectangle

$=$ $600$ $+$ $1500$ Plug in the two areas

$=$ $2100 \text(cm)^2$

Finally, multiply the area by the depth to find the volume

$\text(Volume)$ $=$ $\text(area)$ $times$ $\text(depth)$ Finding the volume

$=$ $2100$ $times$ $12$ Plug in the known lengths

$=$ $25200 \text(cm)^3$

The given measurements are in centimetres, so the volume is measured as centimetres cubed

$\text(Volume)=25200 \text(cm)^3$

Question 2 of 5

Find the volume of the figure

Round your answer to the nearest whole number

Use

$pi=3.141592654$

$\text(Volume )=$ (31616, 31605, 31625) $\text(cm)^3$

Using	Answer
$pi=3.141592654$	$31616 cm^3$
$pi=3.14$	$31605 cm^3$
$pi=(22)/(7)$	$31625 cm^3$

Question 3 of 5

Find the volume of the figure

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Volume )=$ (179.07, 178.98, 179.14) $\text(cm)^3$

Using	Answer
$pi=3.141592654$	$179.07 cm^3$
$pi=3.14$	$178.98 cm^3$
$pi=(22)/(7)$	$179.14 cm^3$

Question 4 of 5

Find the volume of the figure

Note: The cylinder is hollow

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Volume )=$ (2211.68, 2210.56, 2212.57) $\text(cm)^3$

Using	Answer
$pi=3.141592654$	$2211.68 cm^3$
$pi=3.14$	$2210.56 cm^3$
$pi=(22)/(7)$	$2212.57 cm^3$

Question 5 of 5

Find the volume of the figure

Round your answer to two decimal places

$\text(Volume )=$ (508.94, 508.68, 509.14) $\text(cm)^3$

$=$	$10580$ $+$ $21036.10441$	Plug in the two volumes
$=$	$31616.10441$
$=$	$31616 \text(cm)^3$	Rounded to the nearest whole number

$\text(radius)$	$=$	$1/2 times$ $6$

$\text(radius)$	$=$	$3$

$=$	$56.54866$ $+$ $122.52211$	Plug in the two volumes
$=$	$179.07078$
$=$	$179.07 \text(cm)^3$	Rounded to $2$ decimal places

$\text(radius)$	$=$	$1/2 times$ $12$

$\text(radius(Larger Circle))$	$=$	$6$

$\text(radius)$	$=$	$1/2 times$ $12$

$\text(radius(short cylinders))$	$=$	$6$

$\text(radius)$	$=$	$1/2 times$ $3$

$\text(radius(long cylinder))$	$=$	$1.5$

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Quiz summary

Information

1. Question

Hint

Correct!

Volume of a Rectangular Prism

Labelling the given lengths

2. Question

Hint

Nice Job!

Volume of a Rectangular Prism

Volume of a Cone

Labelling the given lengths

3. Question

Hint

Well Done!

Volume of a Hemisphere

Volume of a Cone

Labelling the given lengths

4. Question

Hint

Keep Going!

Volume of a Cylinder

Labelling the given lengths

5. Question

Well Done!

Volume of a Cylinder

Labelling the given lengths

Quizzes

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(width)$
	$=$	$30$ $times$ $20$ $=$ $600 \text(cm)^2$

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(width)$
	$=$	$60$ $times$ $25$ $=$ $1500 \text(cm)^2$

	$=$	$600$ $+$ $1500$	Plug in the two areas
	$=$	$2100 \text(cm)^2$

$\text(Volume)$	$=$	$\text(area)$ $times$ $\text(depth)$	Finding the volume
	$=$	$2100$ $times$ $12$	Plug in the known lengths
	$=$	$25200 \text(cm)^3$

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(breadth)$
	$=$	$46$ $times$ $46$ $=$ $2116 \text(cm)^2$

$\text(Volume)$	$=$	$\text(area)$ $times$ $\text(height)$	Finding the volume
	$=$	$2116$ $times$ $5$	Plug in the known lengths
	$=$	$10580 \text(cm)^3$

$\text(Volume)$	$=$	$1/3 times pi times$ $\text(radius)^2$ $times$ $\text(height)$

	$=$	$1/3 times 3.141592654 times$ $18^2$ $times$ $62$

	$=$	$21036.10441 \text(cm)^3$

$\text(Volume)$	$=$	$1/2 times 4/3 times pi times$ $\text(radius)^3$

	$=$	$1/2 times 4/3 times 3.141592654 times$ $3^3$

	$=$	$56.54866 \text(cm)^3$

$\text(Volume)$	$=$	$1/3 times pi times$ $\text(radius)^2$ $times$ $\text(height)$

	$=$	$1/3 times 3.141592654 times$ $3^2$ $times$ $13$

	$=$	$122.52211 \text(cm)^3$

$\text(Area)$	$=$	$pi times$ $\text(radius)^2$
	$=$	$3.141592654 times$ $6^2$
	$=$	$113.09733 \text(cm)^2$

$\text(Area)$	$=$	$pi times$ $\text(radius)^2$
	$=$	$3.141592654 times$ $2^2$
	$=$	$12.56637 \text(cm)^2$

	$=$	$113.09733$ $-$ $12.56637$	Plug in the two areas
	$=$	$100.53096 \text(cm)^2$

$\text(Volume)$	$=$	$3.141592654 times$ $\text(radius)^2$ $times$ $\text(height)$
	$=$	$3.141592654 times$ $6^2$ $times$ $2$
	$=$	$226.19467$

$\text(Volume)$	$=$	$226.19467 times 2$
	$=$	$452.38934 \text(cm)^3$

$\text(Volume)$	$=$	$3.141592654 times$ $\text(radius)^2$ $times$ $\text(height)$
	$=$	$3.141592654 times$ $1.5^2$ $times$ $8$
	$=$	$56.54866 \text(cm)^3$

$=$	$452.38934$ $+$ $56.54866$	Plug in the two volumes
$=$	$508.938$
$=$	$508.94 \text(cm)^3$	Rounded to $2$ decimal places

Using	Answer
$pi=3.141592654$	$508.94 cm^3$
$pi=3.14$	$508.68 cm^3$
$pi=(22)/(7)$	$509.14 cm^3$